Experimentally constrained ${}^{165,166}\mathrm{Ho}(n,\gamma )$ rates and implications for the $s$ process

The $\gamma$-ray strength function and the nuclear level density of ${}^{167}\mathrm{Ho}$ have been extracted using the Oslo method from a ${}^{164}\mathrm{Dy}(\alpha ,p\gamma ){}^{167}\mathrm{Ho}$ experiment carried out at the Oslo Cyclotron Laboratory. The level density displays a shape that is compatible with the constant temperature model in the quasicontinuum, while the strength function shows structures indicating the presence of both a scissors resonance and a pygmy dipole resonance. Using our present results as well as data from a previous ${}^{163}\mathrm{Dy}(\alpha ,p\gamma ){}^{166}\mathrm{Ho}$ experiment, the ${}^{165}\mathrm{Ho}(n,\gamma )$ and ${}^{166}\mathrm{Ho}(n,\gamma )$ eellian-averaged cross section (MACS) uncertainties have been constrained. The possible influence of the low-lying, long-lived 6 keV isomer ${}^{166}\mathrm{Ho}$ in the $s$ process is investigated in the context of a $2M_{\odot }, [\text{Fe}/\text{H}]=-0.5$ asymptotic giant branch star. We show that the newly obtained ${}^{165}\mathrm{Ho}(n,\gamma )$ MACS affects the final ${}^{165}\mathrm{Ho}$ abundance, while the ${}^{166}\mathrm{Ho}(n,\gamma )$ MACS only impacts the enrichment of ${}^{166,167}\mathrm{Er}$ to a limited degree due to the relatively rapid $\beta$ decay of the thermalized ${}^{166}\mathrm{Ho}$ at typical $s$-process temperatures.

Figure 1

The normalized NLD compared to the theoretical models used in talys 1.96 [10]. For an overview of the models and references, see text. The error bars indicate the statistical and systematic uncertainties from the Oslo method, and the uncertainty band shows the systematic errors from the normalization procedure. The vertical, pink-shaded band (light grey) indicates the region used for fitting the extracted NLD to the known levels of ${}^{167}\mathrm{Ho}$ from Ref. [31].

Figure 2

The normalized GSF compared to the theoretical models used in talys 1.96 [10]. For all the $E1$ models listed in the plot, the $M1$ SMLO [37] was added, except for the $\text{D1M}+\text{QRPA-0lim} E1$ model, where the corresponding $\text{D1M}+\text{QRPA-0lim} M1$ was used [38]. See text for an overview of the models and their references. Uncertainties are as in Fig. 1.

Figure 3

The normalized GSF and the fit to the data using the empirical functions described in the text. The ${}^{165}\mathrm{Ho}$ GEDR data from Varlamov et al. [56] are used fit the GEDR. The dotted line shows the theoretical QRPA predictions for the $M1$ GSF from Ref. [57].

Figure 4

Estimation of the $E1$ strength using a simple exponential passing through two points of the GSF (see text). Data points from this work are shown as black points, while the red line is the modeled $E1$ strength, and the blue area shows the residual strength.

Figure 5

The ${}^{165}\mathrm{Ho}(n,\gamma )$ cross section calculated with the experimentally extracted NLD and GSF for ${}^{166}\mathrm{Ho}$ compared to data from Czirr et al. [63], Poenitz et al. [66], Gibbons et al. [67], McDaniels et al. [65], Asghar et al. [64], Voignier et al. [68], and Lepine et al. [69].

Figure 6

The Maxwellian-averaged cross sections for (a) ${}^{165}\mathrm{Ho}(n,\gamma )$ and (b) ${}^{166}\mathrm{Ho}(n,\gamma )$ using our data as input compared to the talys uncertainty range as well as JINA REACLIB [70] and BRUSLIB [71] (see text).

Figure 7

Elemental surface overabundances [X/Fe] at the end of the AGB evolution of our $2M_{\odot }\left[\text{Fe/H}\right]=-0.5$ model star as a function of the charge number $Z$ for different values of the ${}^{165}\mathrm{Ho}(n,\gamma )$ MACS, namely the upper and lower limits spanned by talys systematics and those constrained by the present Oslo experiment. The Oslo-constrained ${}^{166}\mathrm{Ho}(n,\gamma )$ MACS obtained with the JLM OMP is adopted in all cases.

Figure 8

Isotopic surface overabundances [X/Fe] at the end of the AGB evolution of our $2M_{\odot }\left[\text{Fe/H}\right]=-0.5$ model star as a function of the atomic mass $A$ for different values of the ${}^{166}\mathrm{Ho}(n,\gamma )$ MACS, namely the upper and lower limits spanned by talys systematics and those constrained by the present Oslo experiment using the JLM OMP.